upper bound

简明释义

上限

英英释义

例句

1.In this optimization problem, we need to determine the upper bound for the maximum profit.

在这个优化问题中，我们需要确定最大利润的上界。

2.The algorithm has an upper bound on its time complexity, meaning it will not exceed a certain limit.

该算法的上界在时间复杂度上，意味着它不会超过某个限制。

3.To ensure safety, the upper bound of the weight limit must be adhered to.

为了确保安全，必须遵守重量限制的上界。

4.The mathematician proved that the upper bound of the sequence is finite.

数学家证明该序列的上界是有限的。

5.The upper bound of the data set indicates the highest value recorded.

数据集的上界表示记录的最高值。

作文

In mathematics and computer science, the concept of an upper bound is crucial for analyzing the performance of algorithms and understanding the limits of various functions. An upper bound refers to a value that a function or sequence cannot exceed. For instance, when we talk about the time complexity of an algorithm, we often express it in terms of its upper bound. This means that we can determine the maximum amount of time an algorithm will take to complete based on the size of the input data. Understanding this concept helps us to evaluate the efficiency of different algorithms and choose the most suitable one for a particular problem.Consider the example of sorting algorithms. The bubble sort algorithm has a worst-case time complexity of O(n^2), which serves as its upper bound. This implies that no matter how optimized the implementation is, the time taken by the bubble sort algorithm will not exceed a certain limit relative to the number of items being sorted. In contrast, the quicksort algorithm has an average time complexity of O(n log n), which is a more favorable upper bound. By knowing these bounds, developers can make informed decisions about which sorting algorithm to use based on the expected size of the dataset.The significance of upper bounds extends beyond just sorting algorithms. In optimization problems, we often seek to minimize costs or maximize profits while adhering to certain constraints. These constraints can be represented as upper bounds on resources, such as budget limits or material availability. For example, if a company has a budget of $10,000 for a marketing campaign, this budget serves as an upper bound on their spending. Any marketing strategy must operate within this constraint to be viable.Moreover, in the realm of statistics, upper bounds are essential for establishing confidence intervals and making predictions. When estimating a population parameter, statisticians often calculate an upper bound to provide a range within which they believe the true value lies. This is particularly important in fields like healthcare and social sciences, where making decisions based on data can significantly impact lives and policies. By understanding the upper bounds of their estimates, researchers can communicate the reliability and potential limitations of their findings.In conclusion, the concept of an upper bound is integral to various fields, including mathematics, computer science, economics, and statistics. It helps us understand the limitations of algorithms, manage resources effectively, and make informed decisions based on data analysis. As we continue to tackle complex problems in our increasingly data-driven world, mastering the idea of upper bounds will be essential for anyone looking to excel in analytical thinking and problem-solving. Whether you are a student, a professional, or simply someone interested in mathematics, grasping the meaning and applications of upper bounds will undoubtedly enhance your understanding of the subject and its real-world implications.

在数学和计算机科学中，upper bound的概念对于分析算法的性能和理解各种函数的极限至关重要。upper bound指的是一个函数或序列无法超过的值。例如，当我们谈论算法的时间复杂度时，我们通常用它的upper bound来表示。这意味着我们可以根据输入数据的大小来确定算法完成所需的最大时间。理解这个概念有助于我们评估不同算法的效率，并选择最适合特定问题的算法。考虑排序算法的例子。冒泡排序算法的最坏情况时间复杂度为O(n^2)，这就是它的upper bound。这意味着无论实现多么优化，冒泡排序算法所需的时间都不会超过相对于被排序项数量的某个限制。相比之下，快速排序算法的平均时间复杂度为O(n log n)，这是一个更有利的upper bound。通过了解这些界限，开发人员可以根据数据集的预期大小做出明智的决策，选择使用哪种排序算法。upper bound的重要性不仅限于排序算法。在优化问题中，我们通常寻求在遵循某些约束条件的同时最小化成本或最大化利润。这些约束可以表示为资源的upper bounds，例如预算限制或材料可用性。例如，如果一家公司为市场营销活动设定了10,000美元的预算，那么这个预算就成为他们支出的upper bound。任何市场营销策略都必须在这个约束范围内进行才能是可行的。此外，在统计学领域，upper bounds对于建立置信区间和进行预测至关重要。在估计一个总体参数时，统计学家通常会计算一个upper bound，以提供一个他们相信真实值所在范围的估计。这在医疗保健和社会科学等领域尤为重要，因为基于数据做出的决策可能会显著影响生命和政策。通过理解他们估计的upper bounds，研究人员可以传达其发现的可靠性和潜在局限性。总之，upper bound的概念在数学、计算机科学、经济学和统计学等各个领域都是不可或缺的。它帮助我们理解算法的限制，有效管理资源，并根据数据分析做出明智的决策。随着我们继续应对越来越复杂的问题，掌握upper bounds的概念将对任何希望在分析思维和问题解决方面脱颖而出的人至关重要。无论你是学生、专业人士，还是仅仅对数学感兴趣的人，掌握upper bounds的含义及其应用无疑会增强你对该主题及其现实世界影响的理解。